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Full text of "Flight test method development for a quarter-scale aircraft with minimum instrumentation"

3UDLEY KFOX ^IBBABY 
ioTOBEY, CALIFORK^IA 93943-S0«e 



NAVAL POSTGRADUATE SCHOOL 

Monterey, California 




THESIS 



FLIGHT TEST METHOD DEVELOPMENT FOR 
QUARTER-SCALE AIRCRAFT WITH 
MINIMUM INSTRUMENTATION 


A 






by 






Nicolaos D 


Bamichas 








Mar ch 


1989 




Thesis 


Advisor : 




Richard 


Howard 



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Naval Postgraduate School 



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II. TiTLE (Include Security Classification) 

TIGHT TEST METHOD DEVELOPMENT FOR A QUARTER-SCALE AIRCRAFT WITH MINIMUM 

NSTRUMENTATION 



6 SuPO-EVEN^A'v \0'A-'0\ 

.■■he views expressed in this thesis are those of the author and do not reflect 
:he official policy or position of the Department of Defense or U.S. Govt. 



"8 SuBjECT TERMS [Continue on reverse if necessary and identify by block number) 

Radio-Controlled Aircraft, Instrumentation, Drag 
Polar, Thrust Required, Power Required, Flight 
Test, Wind Tunnel, Torque Stand 



'9 ABSTRACT {Continue on reverse if necessary and identify by block number) 

\ flight test method was developed for a quarter -scale model aircraft with 
ninimum onboard instrumentation for the determination of the Drag Polar, the 
rhrust Required curve and the Power Required curve. The test included a wind 
tunnel test for propeller efficiencies and thrust coefficients, a torque test 
Eor engine shaft horsepower, and a flight test for flight speeds at measured 
Dperating conditions. The only additional onboard instrumentation besides 
that for radio control was a small cassette recorder. Two methods are 
described for data manipulation and an error analysis is provided for each 
nethod . 



DS*=3.*C-. AVA .ASLm V OF A3S*RAC" 
2 .".C-ASS- ED'UNL MTED D SAME AS RPT 



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DDFORM 1473,: 



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SECURITY CLASSIFICATION OF THIS PAGE 



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Approved for public release: distribution is unlimited. 



Flight Test Method Development for a 

Quarter-Scale Aircraft 

with Minimum Instrumentation 



by 

Nicolaos D. Bamichas 
Captain, Hellenic Air Force 

Submitted in partial fulfillment of the 
requirements for the degree of 

MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING 

from the 

NAVAL POSTGRADUATE SCHOOL 
March 1989 



ABSTRACT 

A flight test method was developed for a quarter-scale model aircraft with 
minimum onboard instrumentation for the determination of the drag polar, the 
trust required curve, and the power required curve. The test included a wind 
tunnel test for propeller efficiencies and thrust coefficients, a torque test for 
engine shaft horsepower, and a flight test for flight speeds at measured operating 
conditions. The only additional onboard instrumentation besides that for radio 
control was a small cassette recorder. Two methods are described for data 
manipulation and an error analysis is provided for each of the methods. 



C.l 



TABLE OF CONTENTS 

I. INTRODUCTION 1 

n. BACKGROUND 3 

ffl. EXPERIMENTAL PROCEDURES 7 

A. THE AIRPLANE 8 

B. TORQUE STAND 12 

C. WIND TUNNEL 18 

D. FLIGHT TEST 19 

IV. RESULTS - DISCUSSION 24 

A. PRETEST FLIGHT 24 

B. FLIGHT TEST 26 

C TORQUE STAND 27 

D. WIND TUNNEL 31 

V. ERROR ANALYSIS 45 

VL CONCLUSIONS AND RECOMMENDATIONS 49 

A. CONCLUSIONS 49 

B. RECOMMENDATIONS 50 

1. The Aircraft 50 

2. The Wind Tunnel and the Torque 

Stand Tests 51 



DUDLEY KNOX LIBRARY 
NAVAL POSTGRADUATE SCHOOL 
MONTEREY, CALIFORNIA 93943-6002 



APPENDIX A - AIRCRAFT CHARACTERISTICS 52 

APPENDIX B - FLIGHT TEST DATA 55 

APPENDIX C - DATA TABLES 56 

APPENDIX D - ERROR ANALYSIS CALCULATIONS 59 

LIST OF REFERENCES 64 

INITLAI. DISTRIBUTION LIST 66 



LIST OF TABLES 

Table L Data from Torque Stand Test 56 

Table 2. Data From Wind Tunnel Test 57 

Table 3. Data from Flight Test and Calculations 58 



LIST OF FICLRES 

Figure lA. Quarter-Scale General Aviation Model 

Aircraft 9 

Figure IB. Top View of the Aircraft 9 

Figure 2. e.g. Variation with Fuel Consumption 11 

Figure 3. DvTiamometer 13 

Figure 4. Prony Brake 14 

Figure 5. Torque Stand 16 

Figure 6. Torque Stand 17 

Figure 7. Electric Motor and Thrust Stand in 

the 3.5' X 5' Wind Tunnel 20 

Figure 8. Forces on the Aircraft on Steady Level 

Flight 22 

Figure 9. Power vs RPM 29 

Figure 10. Engine Power vs RPM Curves 30 

Figure 11. Thrust Coefficient vs Advance Ratio 32 

Figure 12. Thrust vs RPM 35 

Figure 13. Propeller Efficiency vs Advance Ratio 36 

Figure 14. Cp vs Cl" 37 

Figure 15. Drag Polar 38 

Figure 16. Thrust Required 40 



Ih 

Figure 17. Pj^V,, vs Wj 42 

Figure 18. Power Required 43 

Figure 19. Side and Top View of the Aircraft 54 



TABLE OF SYMBOLS 



AR 


Aspect Ratio 


b 


Wingspan 


BHP 


Brake Horse Power 


Co 


Drag Coefficient 


Coo 


Parasite Drag Coefficient 


c. 


Lift Coefficient 


Ct 


Thrust Coefficient 


c, 


Chord at the Root 


c, 


Chord at the Tip 


d 


Propeller Diameter 


D 


Aircraft Drag 


e 


Oswald Efficiency Factor 


F 


Force Measured in Torque Stand 


J 


Advance Ratio 


1 


Torque Stand Arm Length 


L 


Aircraft Lift 


mAh 


Milliamperes per Hour 


N 


Revolutions per Second 


P 


Atmospheric Pressure 



P,^ Power Required, corrected for Standard Conditions. Standard 
Weight 

P, Power Required 

Q Torque 

R Gas Constant for Air 

RPM Revolutions per Minute 

S Wing Area 

T Thrust 

T, Thrust Required 

Teo„ Thrust from Wind Tunnel Test, after correction made for the 
torque factor 

T,^ Thrust Reading in Wind Tunnel Test 

V Velocity 

V,^ Velocity for Standard Weight, Standard Conditions 

V, Same as V^^ 

V, Velocity as Obtained from Flight Test 

W Aircraft Weight 

WcD Drag Coefficient Uncertainty 

WcL Lift Coefficient Uncertainty 

Wct Thrust Coefficient Uncertainty 

Wj Advance Ratio Uncertainty 

Wp Power Required Uncertainty 



Wt 


Thrust Uncertainty 


w. 


Standard Weight of the Aircraft 


W, 


Test Weight of the Aircraft 


w^ 


Velocity Uncertainty 


a 


Density Ratio 


CT, 


Test Density Ratio 


P 


Air Density 


Po 


Air Density at Sea Level Standard Conditions 


P. 


Test Air Density 


n 


Propeller Efficiency 


a 


Angle of Attack 


K 


3.1415926 


A 


Sweep Angle 


X 


Taper Ratio (c,/c,) 



ACKNOWLEDGEMENT 

I would like to thank Pat Hickey, Jack King and John Moulton for their 
help during this project. I would like to give special thanks to Don Harvey who 
built the torque stand and helped to build the aircraft, and to Don Meeks whose 
30 years experience in flying radio controlled airplanes, proved to be valuable 
for the flight test. Special thanks also are deserved by my Thesis Advisor Dr. 
Richard Howard who helped me to integrate this work. 

Finally, I would like to thank my family, my parents and everybody else, 
who helped me during these past two years at the Naval Postgraduate School. 



I. INTRODUCTION 

"The unmanned vehicle of today is a technology akin to the importance of 
radar and computers in 1935." [Ref. 1, p. 12] These are the words with which 
Dr. Edward Teller, father of the nuclear age, recently referred to remotely piloted 
vehicles (RPVs). 

The success of the Israelis in the Bekaa Valley in 1982, certify the truth 
of Dr. Teller's words. By flying small RPVs in the Valley, the Israelis 
destroyed 29 surface-to-air Syrian SAM missiles in one single hour [Ref. 1, pp. 
3-4]. 

This success caused many countries to become interested in RPVs and to 
start or accelerate RPV programs which have played a major role in the mihtary 
world in the last few years. 

Low risk, due to lack of human beings on board, makes their procurement 
progress easier. Some, as Pioneer, proceeded without flight test. Therefore, 
many unknowns may exist about the aircraft's performance. 

In this report, a method of flight testing a small radio controlled aircraft 
was developed. The goal was to develop the drag polar and the power 



required curves for the aircraft with minimal onboard instrumentation. 
Instrumentation is very important for small aircraft, where the weight factor is 
very critical—a one or two pound payload increase can be detrimental. 



II. BACKGROUND 

Model Airplanes: To dream, to build, and tiien to fly. 

The roots of their art may go back to ancient Egypt, where a small winged 
object of sycamore was found in 1898 in a royal tomb. Archytas, a 
contemporary of Plato, is credited with flying a mechanical bird successfully 
also, around 400 BC. In 1804, Englishman Sir George Cayley fashioned a 
glider, and in 1871, Frenchman Alphonse Penauh built a stable miniature aircraft 
powered by a rubber band. [Ref. 2, p. 132] 

At Westover Air Force Base in Chicopee, Massachusetts, the rubber band 
still powers aircraft in a model competition category called free flight. Two 
other categories of model aircraft competition are radio control, in which an 
aircraft responds to signals from a transmitter, and control line, where the builder 
manipulates a handle whose wires are attached to the airplane. [Ref. 2, p. 132] 

Today, the technology of radio control systems advances very fast. 
Remotely controlled aircraft earn more and more of the interest of people 
compared to the other two categories. The advanced technology of electronics 
and the ability of building highly advanced sensors integrated into a small size 
that can fit in these small airplanes makes them an important weapon from the 
military point of view. 



During the last 20 years, much research for RPVs has been done and many 
flight tests have been performed. 

In 1975, a propeller and engine testing for mini-remote piloted vehicles 
was performed with wind tunnel and torque stand tests, at the Air Force Institute 
of Technology at Wright-Patterson AFB. 

In 1975, NASA Dry den Flight Research Center flight tested a large-scale 
(3/8) model of an F-15 fighter aircraft, to investigate the stability and 
controllability of the configuration at high angles of attack. [Ref. 3, p.l] 

The same organization, in 1986, developed an experimental flight test 
maneuver autopilot for a .44-scale version of an envisioned full-scale fighter 
aircraft [Ref. 4, p.l], that was designed to increase the quantity of data obtained 
in flight tests. 

In 1976, at a symposium held at the Royal Aeronautical Society in London, 
"RPVs - Roles and Technology," was discussed in a paper by the British Aircraft 
Corporation. Since then, research on the "stabilized" RPV has been 
accomphshed within the United Kingdom UMA Systems Research Programme. 
[Ref. 5, p. 136] 

In 1985, five joined wing RPVs were flight tested at North Carolina State 
University, in order to examine the behavior of these aircraft in flight. [Ref. 6, 
p. 1] 



In 1985, at Mississippi State University, a method was devised to determine 
the propulsive efficiency and aircraft drag from steady state flight test data. The 
method used was based on a computer formulation of Lx)ck's equivalent propeller 
model. [Ref. 7, p. 1] 

At the Naval Postgraduate School, a RPV program sponsored by NAVAIR 
has started. RPV research projects can be used to investigate aerodynamic 
phenomena of interest to NAVAIR with application to the RPV or to other 
aircraft. 

In 1988, a RPV was designed and its construction started for use in 
investigating the feasibility of using the Wortmann FX 63-137 airfoil, as well as 
to improve the stabilit>- and control characteristics of the Pioneer RPV. 

Also in that same year, two model aircraft were delivered to the Naval 
Postgraduate School. A half-scale Pioneer RPV, used for training by the U.S. 
Navy and the U.S. Marine Corps, and a quarter-scale general aviation type 
aircraft were acquired. The program for these aircraft included flight tests in 
order to develop their performance in terms of aerodynamic and powerplant 
characteristics. Wind tunnel tests and measurements of the engine on a torque 
stand were also accomphshed in order to develop a method for flight testing of 
radio-controlled aircraft. 



This report deals with the quarter-scale flight testing and complementary 
tests. The limited payload capabihty of this aircraft necessitated minimum 
onboard instrumentation. 



III. EXPERIMENTAL PROCEDURE 

The goal of the flight test was to obtain the drag polar of the airplane, and 
the thrust required and power required curves. To reach that goal, it was 
necessary to develop the following: 

- Variation of the power with RPM and throttle setting 

- Variation of the thrust that the propeller produces at various flight speeds 

- Variation of the propeller efficiency with the advance ratio 

All of the above requirements were obtained by performing three major 
tests. 

First, a torque stand test was accomplished. In this test, the torque of the 
engine was measured and its power was calculated. By using six different loads, 
the power versus RPM curves were plotted for various throttle settings. 

Using the 3.5' x 5' wind tunnel of the Naval Postgraduate School, the 
propeller thrust coefficient and efficiency variation with the advance ratio were 
developed. 

Finally, a flight test was performed, in order to collect data for the airplane 
in flight. These data consisted of the velocity of the aircraft at every engine 
throttle setting and the RPM. 



The method that will be followed to obtain the drag polar and the power 
required curves, hereafter referred to as thrust method, is as follows: 

Manipulating thrust, velocity and RPM data from a wind tunnel test, will 
provide the Q versus J plot. Then, from that plot, the thrust in flight will be 
obtained through the RPM and velocity measured in flight. The drag and Lift 
coefficients as well as the power required will then be calculated, so that the 
drag polar and the power required curves can be obtained and plotted. 

Another available method to obtain the above results is hereafter referred 
to as the power method. From the power versus RPM plot, obtained from a 
torque stand test, and the propeller efficiency versus the advance ratio plot, 
obtained from a wind tunnel test, the power required and thrust required are 
calculated and plotted as well as the drag coefficient so that the drag polar is 
plotted. These methods will be described in more detail in following sections. 

A. THE AIRPLANE 

The airplane that was used for this fhght test was a quarter-scale general 
aviation type, radio-controlled airplane (Figure 1). Its main components were an 
aluminum tube, to which were attached the foam-core wings and horizontal tail, 
the wooden vertical tail, a 3-HP single- cylinder two-stroke gasoline engine and 
the plastic fuselage. In the plastic fuselage were mounted a 14-ounce fuel tank, 
the radio receiver, the battery and the four servos for the ailerons, the elevator. 




Figure lA. The Quarter-Scale General Aviation Aircraft 




Figure IB. Top View of the Aircraft 
9 



the rudder and steering and the throttle. Mounted to the aluminum tube in the 
fuselage were the two supports for the wings and the main landing gear. 

Before the final adjustment of the push rods for the three control surfaces 
and the throttle could be made, the wing structure and fuselage were located to 
set the proper position of the e.g. at approximately 25% chord. Later on, for a 
known location of the landing gear with respect to the aircraft reference, 
measuring the weight distribution gave the exact e.g. position. Its variation with 
fuel consumption was found to be from 26.25 to 27.52% of the aerodynamic 
chord as shown in Figure 2. Upon completion of the aircraft construction, its 
geometric parameters were measured. The results are shown in Appendix A. 

The engine was a single-cylinder, 40 cc two-stroke gasoline engine, rated 
at 3-HP at a maximum speed of 11000 RPM. 

The propeller that was used for the entire test was a 20-8' wooden 
propeller. Before any tests or flights could be accomplished, break-in of the 
engine was necessary. To do so, the engine was mounted on a wooden stand 
made for this purpose. Break-in consisted of two hours total running, at all 
throttle settings. During break-in, adjustment of the engine was also performed 
to ensure the best performance at low as well as at high RPM. 



^20-8 propeller refers to a 20-inch diameter and an 8-inch 
pitch, the pitch being the distance that the propeller advances in 
one revolution. 

10 




0.0 



2.0 



4.0 6.0 6.0 10.0 

FUEL IN TANK (OZ) 



12.0 



14.0 



Figure 2. e.g. Variation with Fuel Consumption 



B. TORQUE STAND 

To measure the Power of an engine vs RPM, three types of devices are 
commonly used. 

The first one is the dynamometer. It consists of an electric generator to 
which the engine is attached [Ref. 8, pp. 21-22] (Figure 3). When the engine 
drives the generator at various RPM, the generator dehvers electric power. 
Proper instrumentation converts this electric power to that of the engine being 
tested. Dynamometers are the most accurate horsepower measuring devices, as 
well as the most expensive. For such a high RPM engine, an eddy current type 
(at a cost of approximately $25,000) would be necessary for this test. 

The second type of device available to measure the power is the prony 
brake. The prony brake (Figure 4) [Ref. 8, p. 20] is a simple friction device 
which, when clamped to the end of the crankshaft, measures the torque or 
turning moment of the engine. As shown in the figure, the engine is provided 
with a brake drum and brake blocks to which is attached a torque arm. At the 
end of the torque arm a scale measures the applied force. The brake is appUed 
and with the engine turning at the desired RPM, the force which is acting on a 
scale at the end of the torque arm can be measured. Problems of other 
investigators with the prony brake led to the design and construction of the 
torque stand [Ref. 9, p. 38]. 



12 




Figure 3. The Dynamometer 



13 



Brake ten s i on 



/(7nni\c tens 
ADJUSTMENT 




FR I CTI ON 
BLOCKS 



Torque arm 



KN I FE EOeE 



cJ ^^ tf- 



^ Scale 



Figure 4. The Prony Brake 



14 



The principle of operation of the torque stand is that during operation, the 
engine exerts a torque. Measurement of this torque permits the calculation of 
the BHP through the formula: 

BHP = 2*7r*l*F*RPM/33000 (eqn. 3-1) 

where 

33000 = 550 ft-lb/HP * 60 sec/min from RPM 

The torque stand (Figure 5 and Figure 6) was designed by the author and 
built in the facilities of the Naval Postgraduate School. It consisted of an 
aluminum plate attached to a steel shaft which, being supported by two bearings, 
was free to rotate. A torque arm 20 inches long was mounted to the aluminum 
plate. At the end of this torque arm, a load cell was attached, to measure the 
force exerting by the engine torque. The measuring device consisted of the load 
cell, a power supply and a voltmeter. The load cell was a strain gage 
compression type rated up to 10 lbs. It was connected to a bridge with four 
input resistances of 350 ohms each. An initial cahbration with known weights 
was performed and an excitation voltage of 6.743 V was found to give scaled 
linear variation with load. A mechanical scale was used after damage of the 
load cell due to engine periodic strong vibrations. This mechanical scale was 
rated up to 25 lb with a 0] ]h resolution. 

In order to determine the horsepower curve, different loads at every engine 
throttle setting must be used. In this way. a curve of the power versus RPM 



15 



! ^*'/'*^*' 






i B,x. e-^-V'-""'" 




^l-ll^ 



Set scv-ew^ 



IT 

0) 



V^;^'' 



^' 



_ / + !. 



fl=M:; 









-*A- 



Figure 5. The Torque Stand Design 
16 




Figure 6. The Torque Stand 



17 



can be constructed for every throttle setting. Then, by knowing the RPM at 
some throttle setting in flight, the brake horsepower can be obtained for that 
particular configuration. As different loads, six different propellers were used: 
20-8, 18-8, 16-8, 14-8, 11-8 and 10-7. 

C. WIND TUNNEL 

In order for the propeller performance to be determined, i.e., the thrust 
coefficient and efficiency variation with the advance ratio, a wind tunnel test 
was necessary. The 3.5' x 5' wind tunnel of the Naval Postgraduate School was 
used. It is a closed circuit, single return, low speed wind tunnel. 

The advance ratio may be interpreted as the distance traveled forward 
during each propeller revolution (V/N), normalized by the propeller diameter (d) 
[Ref. 10 p. 9]: 

J = V/Nd (eqn. 3-2) 

The thrust coefficient is defined as 

Ct = T/pN2d' (eqn. 3-3) 

Operation of the gasoline engine in the wind tunnel would require the 
necessity of special construction of an apparatus for collecting exhaust gases, 
result in difficulty in starting the engine in the limited space of the test section, 
and create safety problems due to the existence of flammable fuel in the wooden 
wind tunnel. For the above reasons and because the thrust that the propeller 
produces depends only on the RPM and flow velocity and is independent of the 



18 



motor that turns it, an electric motor was used instead of the airplane engine for 
the thrust tests. 

The propeller used in flight was mounted to the electric motor through a 
shaft adaptor. The electric motor was attached to a thrust stand (Figure 7) 
designed by Lieutenant James Tanner [Ref. 11]. This thrust stand consisted of 
an aluminum 18-inch long arm with a window for the attachment of four strsdn 
gages to measure the displacement caused by the thrust force. A proper 
cahbration of the stand with known weights, resulted in a voltage reading 
corresponding to thrust in pounds. A toothed wheel was attached to the motor 
shaft which in combination with a magnetic proximity sensor attached to the 
stand, gave the RPM of the propeller. For more information on the thrust stand 
see [Ref. 11]. 

A variable voltage source played the role of the throttle by changing the 
input voltage to the motor from to 140 volts. In this manner the voltage 
could be varied at a set tunnel speed, and the RPM and the thrust measured, 
to result in a curve of the thrust coefficient versus the advance ratio. 

D. FLIGHT TEST 

To test fly the airplane, various methods and techniques exist. The one 
which will be used depends on what is currently under investigation. In this 
case, with a small scaled aircraft, the goal was to obtain the drag polar and the 
thrust required and the power required as functions of flight speed. 



19 




Figure 7. The Electric Motor and the Thrust Stand in 
the 3.5' X 5' Wind Tunnel 



20 



For the drag polar to be calculated, the variables that are necessary to be 
known are velocity, RPM, and thrust. The lift coefficient in straight and level 
flight (where Lift = Weight) depends on the weight of the airplane (Figure 8), 
the dynamic pressure and the wing area, i.e., 

Q = W/qS = W/^pV2S (eqn. 3-4) 

For known weight and wing area, the only unknown that must be 
determined is the dynamic pressure, and for measured pressure and temperature, 
this unknown reduces to the true velocity of the airplane. 

To calculate the drag coefficient requires more effort. Since the drag 
coefficient C^ is defined as: 

Cd = D/qS = D/^pV^S (eqn. 3-5) 

drag, as well as velocity, must be known. 

Because the flight is straight and level, thrust is equal to drag, i.e., 
T = D 
But from equation (3-3), 

T = CxpN^d' (eqn. 3-6) 

In other words, for constant p and d, Cj and N must be determined. The 
thrust coefficient of the propeller vs advance ratio is known from wind tunnel 
test results The rotational speed N (or RPM) was recorded in flight onboard 
the aircraft. 



21 



i LIFT 




THRUST 



Figure 8. Forces on the Aircraft on Steady Level Flight 



22 



To determine true flight speed, the ground speed course method [Ref. 12, 
p. 4.16] was chosen. This is a method that is used by general aviation aircraft 
to compute the position error of the pitot static system. The method consists of 
runs over a premeasured ground distance. By recording the time it takes for the 
airplane to travel the marked distance, the true Velocity can be calculated. To 
eliminate the effect of any headwind, two runs in opposite directions must be 
conducted. By averaging the two velocities, the wind component cancels out 
with the assumption that it was constant during these two runs. The airplane 
should also be allowed to drift with the cross wind, i.e., the aircraft should be 
allowed to fly on the magnetic heading of the ground course so that the 
crosswind component is eliminated also. Each pair of runs must be 
accompUshed at constant RPM, i.e., constant throttle setting. 

To measure the RPM in flight, a small cassette recorder, weighing seven 
ounces, was mounted inside of the fuselage. A wire was wrapped around the 
spark plug cable so that a periodic electric signal was transmitted by induction 
to the recorder through a shielded cable. Playback of the cassette into a 
frequency counter revealed the frequency of this signal and the RPM of the 
engine. This cassette recorder was the only onboard instrumentation used in this 
flight test. 



23 



IV. RESULTS - DISCUSSION 

A. PRETEST FLIGHT 

An introductory flight was necessary after the airplane had been built. The 
main reason for this is for checkout of any handling problems or trim 
adjustments. A very experienced pilot must be chosen for this very first flight. 

Preflight inspection included: 

Inspection of engine for good condition and to ensure bolt tightness 

Inspection of fuselage for good condition and to ensure tightness of all 
parts (receiver, battery, servos, etc) 

Inspection of correct movement of all control surfaces and engine throttle 

Range test for the transmitter. A 200 ft test with the transmitter antenna 
coUapsed was positive and guaranteed that a much longer range would be 
obtained during flight with the antenna extended. This test was 
accomplished with the engine running, to ensure that there was no 
interference from the engine. A second range test was conducted during 
the taxi test. 

Engine operation at different throttle settings and engine response. The 
engine must run smoothly at 4-cycle operation (low speeds) as well as at 
2-cycle operations (high speeds). 

Taxi test -for good response of the airplane and centered nose wheel 
steering straight taxiing at neutral. A second range test for the transmitter 
was also accomplished during taxiing. 

Shutdown and inspection of the engine for loose bolts or fittings. 

Fuel tank inspection for good condition. 



24 



After the preflight inspection, the first flight was conducted. 
Tests during this first flight were performed in order to certify: 

Control surface response 

Correct trim of the airplane 

Engine response 

Possible frequency interference for the radio 

Effect of e.g. location 

Speed of the airplane at minimum throttle setting 

For this airplane, in accordance with the pilot's recommendations, the 
required adjustments, after this first flight, were elevator trim adjustment and 
movement of the e.g. location from 25% chord to 30% chord. This last 
adjustment was accomplished by adding a small weight behind the e.g. and by 
moving the recorder to the rear part of the fuselage. On subsequent flights, 
instead of the weight, a larger battery of 1200 mAh capacity replaced the 
existing one of 500 mAh. This also gave a longer flight time due to the extra 
battery hfe, and eliminated the possibility for electric power loss in flight. A 
second flight indicated that the addition of the small weight was unnecessary and 
had an undesirable effect on low speed behavior. A third flight, with the final 
configuration of the airplane, gave results that promised a safe test flight for the 
airplane. 



25 



B. FLIGHT TEST 

The flight test data were collected on two different days. The first day, the 
flight test took place at Fritzsche Army Airfield, Fort Ord, California. Runs 
were performed over a premeasured distance of 1500 ft and for throttle settings 
from 8 to 20\ Four persons were used during this flight test to collect the data: 
the pilot and the person that was timing the runs and recording time, throttle 
position and run number, standing at the midway point of the ground course; and 
one person at each end of the ground course, signalling the passage of the 
aircraft and the beginning of the timing. The time for each run was recorded 
on a flight test form, specifically designed for this experiment (Appendix B). 
The ambient temperature and the atmospheric pressure were obtained from the 
nearest airport. The air density was calculated from the equation of state: 
p = p/RT (eqn. 4-1) 

The RPM were recorded by the cassette recorder mounted in the fuselage 
of the airplane. In order to provide correspondence between the RPM and each 
particular run during playback of the cassette, a second recorder synchronized 
with the one in the airplane, was used. Into this recorder, the person recording 
the time announced the start and end of each run as well as each throttle setting 
change. 



^The throttle lever on the transmitter had 23 settings. These 
were set up to correspond to throttle openings from 30% to 100%. 



26 



Every five to six two-pass runs, the airplane was landed for refueling. An 
estimation of the fuel consumption was recorded so that the Velocity could be 
corrected to standard weight by 

V, = V,(WyW,)^(a,)^ = V,, (eqn. 4-2) 

On that day some frequency interference was observed, causing apparent 
problems of piloting the aircraft. This interference was considered serious and 
led to the use of another field, at Los Banos, California, for the second's day 
flight test. 

On the second day of testing, the ground course distance was reduced to 
1000 ft due to the limited ground run distance available. The same 
measurements as for the first day of testing were made, this time for all throttle 
settings. A new temperature and pressure were also recorded. 

After calculation of velocities corrected to standard weight, an average 
velocity and an average test weight were used for further calculations. Values 
of these, as well as RPM data, are shown in Table 1. 

For each test weight and the corresponding velocity, the lift coefficient 
was calculated from eqn. 3-4. 

C. TORQUE STAND 

As mentioned in Chapter III, a torque stand was used to determine the 
power of the engine at various throttle settings and RPM. 



27 



The data recorded are shown in Table 2 and the power curves vs RPM are 
plotted in Figure 9 for the electric motor. From this plot the BHP of the motor 
can be obtained for some particular RPM and throttle setting. This value of 
BHP was used to determine the propeller efficiency from the wind tunnel test 
data for the same throttle setting. 

A large periodic fluctuation of the force reading from the load cell was 
observed, specifically at high throttle settings. Careful search for the cause of 
this fluctuation revealed that the flowfield from the propeller blowing on the 
torque stand was producing a Uft to the torque stand arm. The solution to this 
problem was the installation of a protective panel in front of the arm. As 
indicated by the electric motor power data, this lift gave an error of as much as 
20%. 

Unfortunately, due to strong high-frequency vibrations of the aircraft engine, 
the strain-gage load cell was damaged and a mechanical scale was used in its 
place. This scale had an resolution of 0.01 pound which was considered very 
satisfactory for these measurements. 

A casting failure in the engine crankcase prevented further measurements 
of the aircraft engine, with the protective panel installed.^ Figure 10 shows the 
power curves plotted without the protective panel. (Comparing the shape of 



^The consolation of this misfortune was that the torque stand 
was the last test conducted. All flight test data had been 
collected when the failure occurred. 

28 







■^\ 






/ 




o 






LEGEND 


,--»----_ 






D 20% 1 




RO 


rii. 


E 


^-« 






o 30%' 




ilo 


ITI 


r~ 


,^' 






A 40% ■ 




id 


TL 


? 


h' 




to 


"i'"5d%1 


"" 


RO 


rtL 


i"'" 




6 


X 60% ' 


r 


^0 


•^1. 


•; 


...v 


'h. 




70%-1 


r 


RO 


r^L 


E 


y' ''"■■•■•. 






V 00% ' 


"^ 


RO 


ri. 


T— 


7' 


''b 


^^ 


8 00% TilROrtLE 






Oh 


H '100% Til Ron LE" 




'"■7 






^ ~-*^ 




K d 


— 1 _^^^ 




W 


y^ ^^\ 




&= 


«^ \ 




o 




X 


0. 




\ 


^ 


X -X 


^^.v— ^ 


\ 


°" 


\ 




,^^.. ^ 


V 


d' 


«,« <>: "» «> 












d_ 


cs 







, 


, , 



Figure 9. Power Versus RPM 



29 



n- 










LEGEND 




□ 30% THROTTLE 






in 


o 40% TI m 1 LE 






CM 


^ 50% T Rb' TLE 


51 






"+"'60% T RO TLE"" 


^j>...;^-^. 






X 70%trROrLE 




'"« 




o 00% TI ROT' LE 


A 


■v^ 


o 


V 90% T {ROT "LE 




v 




:?::ioQ%THi^mE:: 


A~^ 




W -5- 




CQ 




v^ 










o 




A 




-4- 


o 






n 




0. 




d- 




GO 




o 


tftg 






d_ 


1 1 1 1 


1 1 1 r- 


1 



1000 2000 3000 4000 5000 6000 7000 0000 9000 10000 

RPM 



Figure 10. Engine Power Versus RPM 



30 



these plots with the one of the electric motor plots, the effect of the flowfield 
from the propeller can be observed.) 

D. WIND TUNNEL 

The last set of data was obtained from the wind tunnel test. The 
temperature and pressure were recorded from the thermometer and barometer of 
the wind tunnel. The conditions were measured to be T = 63°F and P = 30.38 
in Hg. Three runs were performed, at three different wind tunnel velocities of 
40.4, 60.06 and 73.67 ^s in an attempt to get a wider distribution of J. At each 
run the thrust and the RPM were recorded for each throttle ( or voltage ) setting. 
The results are shown in Table 3. From the reading of the voltmeter for the 
thrust, a correction was made for engine torque. Specifically, part of the reading 
was due to the actual torque of the motor. To correct for this, the voltage 
measured at the torque stand was subtracted from the voltage reading of the 
wind tunnel so that the corrected thrust corresponds to pure thrust of the 
propeller. 

In accordance with eqn. 3-2 and eqn. 3-3, the advance ratio and the thrust 
coefficient were calculated (Table 3) and the Q vs J curve was plotted (Figure 
11). To fit the data in this plot, the curve fitting method of least-square 
regression was used. Looking at this Figure, a considerably large scatter can be 
observed. One reason for the scatter can be attributed to the electric motor. 
The 20-8 propeller proved to be a heavy load for this 1-HP motor causing it to 



31 




0.50 



Figure 11. Thrust Coefficient Versus Advance Ratio 



32 



overheat, which tended to reduce RPM. To minimize the temperature effect, 
one to two minute intervals with the electric motor stopped were taken between 
each throttle setting to allow the engine to cool down by the wind tunnel air 
flow. 

Another reason for the data scatter is due to the error in reading the RPM. 
At high throttle settings, a significant thrust change corresponded to a very small 
RPM change, as can be seen in the thrust versus RPM plot (Figure 12). Since 
in eqn. 3-3 the RPM are squared, the result gives a large scatter for those points. 
An extended error analysis relating to the scatter is given in Chapter V, Error 
Analysis. It is considered that more runs at various wind tunnel velocities at 
throttle settings up to 80% would give more precise data. 

The efficiency of the propeller was calculated from the formula 
r| = T V/BHP 550 (eqn. 4-3) 

where BHP was obtained from the BHP versus RPM plot (Figure 9) by entering 
with the RPM corresponding to each value of thrust T and knowing the throttle 
setting at which they were obtained in the wind tunnel. 

The plot (Figure 13) gives a maximum propeller efficiency of 83% at an 
advance ratio of about .32 and 0% at 0.495. This reveals that to have best 
results the aircraft should fly in the advance ratio regime from 30 to 0.35. 
The large scatter that is observed in this plot is attributed to the same causes as 
for the Ct vs J diagram. 



33 



^ 
















o_ 












A 

A 




00- 




LEGEND 




D 


= 73.67 EPS 








O 






O 


= G0.06 EPS 












H 
in 

H 


A 


= 40.40 EPS 








^ O 






A 


A 


A 


A 

o 


o 
o 

D 


D 
D 






^-^ 


^ 


o 

O 




□ 




1 










d^ 


D 




CO 
1 "T 




.... , j_. J . 




r 




"I 1 





1000 EOOO 3000 4000 5000 6000 70 

RPM 



00 



Figure 12. Thrust Versus RPM 



34 




0.25 0.30 



Figure 13. Propeller Efficiency Versus Advance Ratio 



35 



The above two curves with the flight test data form the basis for the 
development of the drag polar, the thrust required and the power required curves. 

As shown in Chapter III, Cl can be calculated from eqn. 3-4 and from eqn. 
3-5. 

Then from eqn. 3-6 the thrust can be calculated as follows: 

For a certain velocity from flight test data (Table 1) and the corresponding 
RPM, the advance ratio can be calculated (eqn. 3-2). Using this advance ratio 
in the Cj vs J plot (Figure 11), the thrust coefficient is obtained. Then from 
eqn. 3-6, the thrust can be calculated and from eqn. 3-5, the drag coefficient. 

Since the drag polar equation can be assumed to be parabolic [Ref. 13, pp. 
211-215] of the form 

Cd = Cd„ -h C^^/neAR (eqn. 4-4) 

If Cd is plotted versus Q^, the resulting line should be straight, based on the 
parabolic assumption. By curve-fitting those data (Figure 14), the drag polar 
equation is obtained (as shown in Figure 15): 

Cd = .045 + .0640Cl2 (eqn. 4-5) 

From the drag polar equation, the parasite drag coefficient has a value of 

Coo = .045 
and from l/rreAR = .0640 the Oswald efficiency factor is found to be 

e = 0.69 



36 




Figure 14. C^ 



.05 
Versu 


0.10 
s C 2 


0.15 

CL2 



0.20 0.25 0.30 



37 




0.00 0.02 



0.04 



0.06 0.00 

CD 



0.12 



0.14 



Figure 15. Drag Polar 



38 



Equation 4-5 was obtained with least square regression. The large scatter 
of the above two plots, raises the question of the cause of the inaccuracy. A 
discussion is given in Chapter V., Error Analysis. The procedure to determine 
the thrust required and the power required curves follows next. 

From eqn. 3-6, the thrust was calculated for each velocity and the thrust 
required was plotted (Figure 16). For the lower part of the curve to be plotted, 
where no data points exist from the flight test, the use of the parabolic drag 
polar is practical, if only as a rough prediction. The reason that no data were 
obtained at that regime was lack of icnowledge of the low speed behavior of the 
aircraft. Lower flight speeds will be investigated in later tests. 

The thrust required curve gives a maximum thrust of 4.5 lbs at 110 fps 
velocity. The minimum thrust required can be calculated by using the drag 
polar, because (CiyCD)„„ takes place at minimum drag [Ref. 13, pp. 255-262]. 

From eqn. (4-5), (CJCj^)^^ can be estimated. This happens when 

Cdo = Q^MeAR 
The above relation gives (CJC^)^^ = 9.32 when Q = 0.839 and C^ = 0.0901. 
Then, since 

V=(W/V2pQS)^ 
the velocitv for (CJC^^)^^ can he calculated and i<: found to be 

V,a,/cD,^x = 49.88 fps 



39 




40 60 00 

VELOCITY (FPS) 



120 



Figure 16. Thrust Required 



40 



At that velocity the minimum thrust is 

T^ = 1.77 lbs 

Since 

P, = TV/550 (eqn. 4-6) 

for each value of thrust, a corresponding power required value was calculated. 
To plot the power required curve, use of Pj^V,^ versus Vj/ was made, which 
is a straight line based on the following development [Ref. 12, p. 5.12]. 

P,, = DVJ550 = V,,(^pV,,2SCd)/550 = (v,pV,,'S/550)(CDo + QVjreAR) 
= KIV,^^ + K2A^,, (eqn. 4-7) 

Therefore: 

P,,V,, = K\W,J + K2 (eqn. 4-8) 

which is the equation of a straight line if Pj^Vj^ is plotted against Y^J. By using 
least square regression for the data points, this equation is found to be 

P^^V^^ = 6.0621 + 6.2706E-7 W,J 
This plot is shown in Figure 17. From this plot the power required curve can 
be plotted (Figure 18). To calculate the minimum power required, use of the 
drag polar equation was made again. Minimum power required happens when 
Q'^/Cd is a maximum [Ref. 12, p. 5.13], at which condition 

C^ = C,,^/7reAR 
This was found to give (Q'^/CJ^a. = 9.72 at Q = 1.453 and Q = 0.1801. This 
high Cl value is probably unobtainable in this low Reynolds number aircraft; 



41 



PIW*VIW 

50 75 



100 



125 




Figure 17. P,,, Versus V,„^ 



42 



q 






















B / 


CO 










D fY^^ 


d~ 










uS 


E^ 










/ 


X 










7 ° 


^ ' CD 










/ ° 


^ 6- 








°/ 




W 








/ 




^ 






/ 






o 






/ 






Cu 






n 






"* 












d" 


/ 


D 








OJ 


\^ ^^/^ 










d- 












o 












d _ 














1 1 1 


1 






1 



20 



40 60 80 

VELOCITY (FPS) 



100 120 



Figure 18. Power Required 



43 



probably the minimum power required value cannot be reached for steady level 
flight. Following the same procedure as for the thrust required, the velocity 
and the drag were calculated for those values. They were found to be 

V = 37.9 fps and D = 2.04 lbs 

Then the minimum power required from eqn. 4-9, is found to be 

P.^ = 0.216 HP 
As mentioned before, data at the lower part of the curve were not obtained due 
to lack of knowledge of the low speed behavior of the aircraft. 

Also from the power required plot, the maximum velocity of the aircraft 
can be estimated at a value of about 110 fps. This happens at a maximum 
power required of approximately 0.8 5 -HP. An accurate value for the maximum 
velocity can not be determined, because the power available curve is not known. 
Such should be obtained from sawtooth climb or acceleration method tests. 



44 



V. ERROR ANALYSIS 

In this chapter, a discussion of the types of errors that may have occurred 
while collecting the experimental data will be presented, for both the Thrust and 
the Power methods, as defined in Chapter ID. Also discussed, will be the 
uncertainty that these errors give to the variables that are used in development 
of the drag polar, the thrust required and the power required. The method that 
is used to obtain the results that follow, as well as sample calculations, are from 
Ref. 14, pp. 48-57, and can be found in Appendix D. 

As described in the previous chapter, the measurements taken during the 
flight test were the time for each run and the RPM from the cassette recorder. 
Uncertainty for the time is estimated to be ±0.3 seconds and can be attributed 
to: 

human error by the person that was timing 

human error by the person that indicated the passage of the airplane from 
the beginning or the end of the run 

flight of the aircraft not absolutely straight and level 

allowance of the aircraft to drift with the crosswind 

Uncertainty for the RPM is estimated to be ± 2% and can be attributed to: 

noise of the recorded signal due to engine operation and the receiver and 
servos 



45 



vibrations from the engine which caused the signal to be ill-timed during 
playback 

actual change in the RPM during the test run 

frequency counter resolution error 

To compare the effect of the ground course distance on the uncertainty of 

the variables, two values are given in each of the following cases: One for 1000 

feet, which was the actual distance on the second day of flight testing; and one 

for 2000 feet, which is considered as the suggested distance. 

For the velocity from V = distance/time: 

uncertainties were found to be: 

Wv = ±3% for a distance of 1000 feet 

Wy = ± 2% for a distance of 1500 feet 

Wv = ± 1.5% for a distance of 2000 feet 

For the advance ratio from J = V/Nd: 

W; = ± 3.6% for 1000 feet 

Wj = ± 2.5% for 2000 feet 

For the thrust coefficient from the Q vs J plot (Figure 11): 

Wct = ± 52% for 1000 feet 

Wer = ± 33% for 2000 feet 

For the thrust from T = C^pN^d": 

Wt = ± 52% for 1000 feet 

Wt = ± 33% for 2000 feet 



46 



For the drag coefficient from C^ = TA^V^S: 

WcD = ± 52.7% for 1000 feet 

WcD = ± 33% for 2000 feet 
For the lift coefficient from Q = WA^pV^S: 

WcL = ± 6% for 1000 feet 

WcL = ±3% for 2000 feet 
For the power required from P, = TV/550: 

Wp = ± 52% for 1000 feet 

Wp = ± 33.2% for 2000 feet 
The above very large values of the uncertainties give an explanation for the 
large scatter of the drag polar data. 

By following the Power method, as described in Chapter III, to calculate 
the drag polar and the thrust and power required curves, smaller values of 
uncertainties are obtained. 

Estimating a ± 1.7% uncertainty for BHP attributed to 
RPM uncertainty 
measuring device uncertainty 
reading error of the plot 



47 



the following results are obtained: 

WcL = same as before 

WcD = ±33.5% for 1000 feet 

WcD = ±12.5% for 2000 feet 

Wt = ±32.8% for 1000 feet 

Wt = ±23% for 2000 feet 

Wp = ±33% for 1000 feet 

Wp = ±23.2% for 2000 feet 

This method gives more accurate results for C^ and T. The reason for this is 

that the Cj vs J plot, which is the major source of uncertainty in the Thrust 

method, is not used. The P, shows the same uncertainty as in the Thrust 

method. The reason for this, is the use of the r| vs J plot (Figure 13) at low 

propeUer efficiency values where the curve is steep and the uncertainty of the 

X] is large (±33%). Use of a propeller more efficient at those values of J will 

reduce potential errors. 

Suggestions to improve the accuracy of the first flight test method are: 

The ground course distance should be increased to at least 2000 feet. 

The pilot should stay at one end of the runway so that he has a better 
view of the airplane's constant heading. 

A noise filter should be constructed and placed before the recorder so that 
the signal will be clearer. 

The recorder should be better isolated from engine vibration. 



48 



VI. CONCLUSIONS AND RECOMMENDATIONS 

A. CONCLUSIONS 

The purpose of this project was to develop a method to estimate the 
performance of a quarter-scale general aviation aircraft with minimal onboard 
instrumentation. In other words, the development of the drag polar and power 
required curves was required. As shown in the previous chapters, a method was 
demonstrated. The drag polar, as shown in Figure 15, was developed and the 
power required versus the true velocity was plotted (Figure 18). Onboard 
instrumentation in flight consisted of a small cassette recorder. 

Three major tests were performed in order to reach the goal: the torque 
stand test, from which the power of two engines, the airplane engine and the 
electric motor, were obtained; the wind tunnel test, which was used to develop 
the propeller efficiency and the thrust variation with the advance ratio; and 
finally, the flight test, during which the velocities of the aircraft at various RPM 
and throttle settings were recorded. 

Manipulation of the data by classical methods produced estimations for the 
drag polar and the power required curves. Observation of the drag polar shows 
a large scatter for the data points. As was explained in Chapter V, Error 
Analysis, this was mainly attributed to the values of the advance ratio for which 



49 



the airplane flew, where a large uncertainty for the thrust coefficient exists. 
Also, in that regime, the propeller efficiency was found to be very low (35- 
45%); use of a more suitable propeller should reduce the scatter to an acceptable 
level. 

From the drag polar, the (CJCo)m«x was estimated and found to be 9.32. 
For those Q and Cp values, the minimum thrust (or drag) of the airplane was 
calculated and found to be T^=1.77 lbs at a velocity of 49.88 fps. Also, the 
(Cl'^/Cd)^^, was estimated and for a value of 9.72, the corresponding minimum 
power required was found to be 0.216 HP at a velocity of 37.9 fps. 

From the power required curve, a maximum velocity of approximately 
110 fps can be estimated at a maximum power required of about 0.85-HP. This 
corresponds to 2.6 BHP, since the propeller efficiency at that speed is only 33%. 

B. RECOMMENDATIONS 

In view of the above conclusions, the following recommendations are made: 

1. The Aircraft 

Use of a more optimum propeller 

Use of a minimum of a 2000-foot ground test distance for future tests 

Installation of a noise filter onboard, which will ^ive a clearer signal and 
will reduce the uncertainty for the RPM 

Isolating the vibration caused by the engine, by installing some special 
device, i.e., lord mounts. This may cause a problem with the e.g. location 
(which will necessitate the need for a small weight addition at the rear part 
of the aircraft), but it is considered a must. 

50 



During the flight test, the pilot <;houl(i stay at one end of the nmway, so 
that he can better maintain a constant heading of the aircraft. 

Ry the airplane at lower speeds and fill in the gaps in the data. 

2. The Wind Tunnel and the Torque Stand Tests 

Select a better and more accurate controller and electric motor. 

Select a more suitable mechanical scale for the torque stand. 

Use the Power method as discussed in Chapter V, Error Analysis, for data 
manipulation. 



51 



APPENDIX A 

AIRCRAFT CHARACTERISTICS 

After measuring the aircraft the following have been obtained. 

Gross Weight W = 16.5 lbs 

A/C length 1 = 4.8 ft 

Wing area S = 6.65 ft 2 

Wing span b = 6.94 ft 

Aspect Ratio AR = 7.25 

Airfoil : Symmetric 

Chord c = 14.2 in 

Wing Incidence Angle = 0.9° 

Leading edge sweep angle A^^ = 1.4° 

Taper ratio X = 0.58 

Fuel weight 14 oz. 

Horizontal tail area Si^^ = 162.3 in 2 

Horizontal tail span b^ = 30 in 

Horizontal tail leading edge sweep angle A^^ = 6.6° 

Horizontal tail taper ratio X^ = 0.66 

Vertical tail area S^r = 9.95 in 2 



52 



Vertical tail span bvr = 9.8 in 
Vertical tail taper ratio X^ = 0.32 



53 




13.9 15. A 28.1 54.3 59.2 




Figure 19. Top and Side View of !he Aircraft 
54 



APPENDIX B 

FLIGHT TEST FORM 



II RUN 1 THROTTLE 1 TIME 1 VELOCITY 1 RPM 1 OTHER II 
II # 1 SETTING 1 IrUN I AVG 1 1 II 


II A 1 1 1 1 1 1 II 


II 1 1 1 1 1 1 1 II 
II B 1 1 1 1 1 1 II 


II A 1 1 1 1 1 1 II 


II 2 1 1 1 1 1 1 II 
II B 1 1 1 1 1 1 II 


II 1 1 1 1 1 1 11 
II A 1 1 1 1 1 1 II 


II 3 1 1 1 1 1 1 II 
II B 1 1 i 1 1 1 II 
II 1 1 1 1 1 1 II 


II A 1 1 1 1 1 1 II 
II J 1 1 till II 


II B 1 1 1 1 1 1 II 
II 1 1 1 1 1 1 II 


II A 1 1 1 1 1 1 II 


II 5 1 1 till II 
II B 1 1 1 1 1 1 II 
II 1 1 1 1 1 1 II 


II 1 1 1 1 1 1 II 
II A 1 1 1 1 1 1 II 


II 6 1 1 1 1 1 1 II 
II B 1 1 1 1 1 1 II 


II A 1 1 1 1 1 1 II 


II B 1 1 1 1 1 1 II 


II A 1 1 1 1 1 1 II 


II B 1 1 1 1 1 1 II 
II B 1 1 1 1 1 1 II 


II A 1 1 1 1 1 1 II 


II y 1 1 1 1 1 1 II 

II B 1 1 1 1 1 1 II 


II A 1 1 1 1 1 1 II 


!! B ! ! ! ! ! ! !! 



Temperature 



55 



APPENDIX C 

DATA TAJBLES 

TABLE 1. TORQUE STAND ELECTRIC MOTOR DATA 



PROP SIZL 




10-7 




11-8 




14-8 




% TiiRorrLn 


RPM 

(lb) 


F Blip 


RPM 

(lb) 


F 


Blip 


RPM 

(lb) 


I^ 


Blip 


20 


3670 


.03 .039 


3230 


.03 


.034 


2280 


03 


.024 


30 


5150 


.04 .073 


4525 


.05 


.080 


3390 


0(> 


.067 


40 


6425 


.06 .137 


5720 


.08 


.149 


4425 


10 


.149 


50 


7665 


.08 .217 


6870 


.10 


.243 


5365 


14 


.206 


60 


8 830 


.10 .313 


8000 


.14 


.360 


6240 


19 


.413 


70 


9890 


.12 .420 


8850 


.17 


.512 


7015 


25 


.601 


SO 


lOSSO 


.15 .578 


9830 


.19 


.662 


7760 


29 


.800 


90 


11700 


.18 .746 


10550 


.22 


.822 


8240 


33 


.980 


100 






11080 


.26 


1.021 


86()0 


^8 


1.165 


PROP SIZP: 




16-8 




18-8 




20-8 




Vo THROTTLE 


RPM 

(lb) 


F Blip 


RPM 

(lb) 


F 


Blip 


RPM 

(lb) 


F 


Bill 


20 


1720 


.04 .024 


1490 


.04 


.016 


1365 


04 


.015 


30 


2715 


.07 .067 


2325 


.07 


.049 


2140 


08 


,053 


40 


3630 


.13 .149 


3135 


.14 


.140 


2875 


14 


. 132 


50 


4425 


.17 .266 


3875 


.20 


.257 


3520 


21 


.249 


60 


5175 


.24 .413 


4455 


.26 


.394 


4065 


28 


.388 


70 


5920 


.30 .601 


5100 


.33 


.573 


4650 


34 


.543 


80 


6460 


.36 .800 


5500 


.40 


.770 


4900 


42 


.719 


90 


6860 


.41 .980 


5605 


.47 


. 913 


5100 


48 


.849 


100 


7000 


.471.165 


6000 


.52 


1.105 


5400 


53 


1.033 



56 



TABLE 2. WIND TUNNEL DATA 



THROTTLE 


\ 


= 73 


.67 fps 




V 


= 60.06 Fps 




\' = 


= 40.4( 


fps 




SETTING 


RPM 


^read 


Tcoir 


J 


RPM 


Tri:ad 


Tcorr 


J 


RPM 


Trrad 


1 corr 


.1 


% VOLTAGE 


(lb) 


(lb) 






(lb) 


(lb) 






(lb) 


(lb) 




10 


4310 


-4.82 


-4.82 


.615 


3270 


-2.67 


-2.67 


.661 


2170 


-1.30 


-1.30 


.670 


10 23 


4380 


-4.68 


-4.68 


.606 


3350 


-2.57 


-2.57 


.645 


2300 


-1.14 


-1.14 


.630 


20 36 


4450 


-4.43 


-4.46 


.596 


3450 


-2.27 


-2.30 


.627 


25(.)0 


- .84 


-.868 


.580 


30 49 


4585 


-4.13 


-4.23 


.578 


3665 


-1.67 


-1.78 


.5^0 


2S15 


- .14 


-.245 


.520 


40 62 


4825 


-3.33 


-3.33 


.550 


3950 


.77 


-.975 


.547 


3240 


.96 


.755 


.45'.) 


50 75 


5110 


-2.33 


-2.66 


.519 


4360 


.63 


.304 


.496 


3770 


2.61 


2.284 


.386 


60 88 


54S0 


-0.73 


-1.18 


.484 


4800 


2.23 


1.774 


.450 


4285 


4.51 


4.o^> 


.340 


70 101 


5810 


1.07 


.480 


.456 


5255 


4.28 


3.693 


.411 


4790 


6.76 


6.173 


.300 


80 114 


6250 


3.17 


2.460 


.424 


5650 


6.58 


5.875 


.383 


5220 


8.91 


8.195 


.280 


90 127 


6290 


4.37 


3.550 


.422 


5700 


8.13 


7.300 


.379 


5330 


10.76 


9.935 


.273 


100 140 


6250 


5.77 


5.62 


.424 


5700 


9.23 


8.350 


.379 


5350 


10.86 


9.980 


.272 


T = 61.9 ° 


F 
























r = 30.16 


n Hg 
























An 
-^ = 0.9482 



























57 



TABLE 3. FLIGHT TEST DATA AND RESULTS 



THROTTLE 














SETTING 


V 

(fps) 


RPM 


T 

(lb) 


Q 


Q 


BMP 


(UP) 


5 


67T70 


5400 


2.00 


.056 


.458 


.640 


.243 


6 


67.200 


5450 


2.27 


.064 


.456 


.690 


.277 


7 


83.870 


6500 


2.04 


.037 


.297 


1 .04 


.323 


8 


89.420 


7080 


2.81 


.044 


.2.59 


1.34 


.457 


9 


92.500 


7380 


3.55 


.052 


.241 


1.61 


.597 


10 


96.180 


7680 


3.84 


.053 


.223 


LSI 


.671 


11 


98.520 


7900 


4.13 


.054 


.212 


1.97 


.740 


12 


103.18 


8100 


3.34 


.040 


.193 


2.05 


.627 


13 


102.92 


8220 


4.41 


.053 


.193 


2.23 


.825 


14 


106.73 


8340 


3.36 


.037 


.183 


2.17 


.652 


15 


103.89 


8400 


5.28 


.062 


.192 


2.49 


.997 


16 


107.43 


8480 


4.03 


.044 


.179 


2.38 


.787 


17 


107.43 


8540 


4.19 


.046 


.179 


2.34 


.818 


18 


106.60 


8550 


4.84 


.054 


.181 


2.50 


.938 


19 


109.85 


8700 


4.24 


.044 


T71 


2.49 


.847 


20 


111.05 


8700 


3.78 


.039 


.167 


2.54 


.763 


21 


109.55 


8700 


4.35 


.046 


.173 


2.48 


.866 


23 


106.64 


8670 


4.97 


.055 


.183 


2.35 


.960 



58 



APPENDIX D 

ERROR ANALYSIS CALCULATIONS 

ir}=A', ♦ A\—A\ 

then uncertainty for Y is: 

where n>i.vv>2,— vv>„ are tlie uncertainties for X^X-^—X^ 

Then by estimating a .3 second error for a run with velocity 100 fps, the following cal- 
culations can be made to estimate the uncertainties using Formula 5-1. 

r = -y-= 100 fps 

Then for a ground distance d = 1000 feet 

dV d looo 



di 


11 1"" 

~ r~~ 10.^ 


- = -10 


n-i- = 


± .3 or 3^0 




Uj = 


= (lOj(.3) = ±3 


or ±y/o 


For distance d = 


1500 feet 


d\- 
dt 


15nn 
15^ 


6.67 


ivY = 


= ± .3 or ± 2''/o 





I vv>=(6.67)(.3) = ±2or2% 
For distance d = 2000 feet 



59 



dt 


•=■ 


2000 
20^ 


5 






»7 = 


= ± 


.3 or ±1.5"/, 








Wy = 


= (■ 


-5K.3)=I.5 


Vo 






So 












For 


d 


= 1000 feet 


^ 


Wv = 


: 3% 




d 


= 1500 feet 


- 


Wy = 


: 2% 




d 


= 2000 feet 


-. 


Wy = 


1.5% 



Estimating a + 2% uncertainty for tlie revolutions of the engine, tlie following cal- 
culations can be made for the run with throttle setting 12. 1 he calculations are made 
for distance 1000 feet. Results in parenthesis are for d = 2000 feet. 



Nd 135 20/12 

dJ _ 1 
6 V i\d 

SI (0.6) r 

-Itt = - -^-4- = - 0.0034 

vv>{103.18)(.03) = 3095 (1.548) 

vi-^=(135)(.02) = 2.7 

wj = [(.0044)^(3.095)^ + (.0034)^(2.7)^]''^ = 0.0164(0.01 14) or 3.6''.o (2.5%) 

From Cr vs J plot (Figure 11), the above values of J give a Wcr = 52" o (33''/o). Then 
further calculations give 

T=CrpNV = 3.3A 

60 



^-pAV = 334 



cC 



cT 



^,. - 2C7/)A"/ = .0495 



ncr={Ol){.52} - .0052%(.0033) 

u^.= (135)(.02) = 2.7 

vvY= [(334)^(.0052)^ + (.0495)^2.7)^]"^ = 1.74 (I.I 1) or 52% (33^/o) 

^ T 



\ lipids 



-=.04 



^^ lIlpV^S 
cCo T 



= .012 



-.00077 
c» l/4pr'5 

»wy=(3.34)(.52)= 1.74(1.10) 
u,(I03.18)(.03) = 3.09 (1.55) 

u-^^ = [(.012)^(1.74)^ + (.00077)^(3.09)^]''^ = .021(.013) or 52.7% (33%) 
= .193 



1/2/) r'5 



-=.0037 



uv= 3.09 (1.55) 

He/: =.01 15 (.0057) or 6^0 (3%) 



61 



''=^--'^" 



dT 550 

dP _ T 
dV 550 

vi.y= 1.74(1.11) 
wv= 3.09 (1.55) 
wp = [(.1876)^(1.74)^ + (.006)^(3.09)^]''^ = .33 (.21) or 52% (33.2ro) 

By using the Power Method as described in Chapter 5, and by estimating from the 
Blip vs RPM plot, a Wbhp = ± l-7"o. Also from the v vs J plot (Figure 13), the uncer- 
tainty for V is estimated to u; = + 33'/o (23%) 

Then, 

/' = ;,BHP = .62 

4^= BMP = 2.05 

,v^^^^ = (2.05)(0.17) = .035 
H-^ = (.305)(.33)=l(.07) 

a> = [(.305)^(.035)^ + (2.05)^(.l)^]'^^ = .205(.144) or 33% (23.2%) 



62 



r=i^=3.34 



4f = -^ = 5.33 
cP \ 



r y2 -^^^ 



wp = .205 (AAA) 

vvt.= 3.09 (1.55) 

ny= [(5.33)^(.205)^ + (.032)^(3.09)^]'^^ = 1.1(.77) or 32.8% (23ro) 



Il2pl-S 
cCn .... 



-—^ = - 00077 



uy=l.l(.77) • 

vwj.= 3.09 (1.55) 

^^CD = [(.012)^(1.1)^ + (.00077)^(3.09)^]"^ = .0134 (.0093) or 33.5ro(23.3%) 



63 



LIST OF REFERENCES 



1. Parker, H. Keith, The Design and Initial Construction of a Composite RPV 
for Flight Research Applications, Master's Thesis, Naval Postgraduate 
School, Monterey, California, October 1988. 

2. Long, M., Model Airplanes, National Geographic, July 1986. 

3. Hollerman, E., NASA Technical Note D-8052, Summary of Flight Tests to 
Determine the Spin and Controlability Characteristics of a Remotely 
Piloted, Large-Scale (318) Fighter Airplane Model, January 1976. 

4. Duke, E., Jones, P., RoncoH, R., NASA Technical Paper 2618, Development 
and Flight Test of an Experimental Maneuver Autopilot for a Highly 
Maneuverable Aircraft, January 1986. 

5. Coleman, R., Robins, A.J., Frary D.J., and Stephenson R., Mini RPV 
Research, August 1980. 

6. Perkins, J.N. and others. North Carolina State University, Report AIAA- 
85-0275, The Design and Testing of Several Joined Wing RPV's, January 
1985. 

7. Bull, G., Bennett, G., Propulsive Efficiency and Aircraft Drag Determined 
from Steady State Flight Test Data, paper presented at the General Aviation 
Aircraft Meeting and Exposition, Wichita, Kansas, April 1985. 

8. Karvinen, Cargnino, Aircraft Propulsion Powerplants, October 1950. 

9. Sanders, Milton R., Propeller and Engine Testing for a Mini-Remote Piloted 
Vehicle, Master's Thesis, Air Force Institute of Technology, Wright- 
Patterson AFB, Ohio, March 1975. 

10. Carson, Bernard H., Wind Tunnel Tests of Unmanned Aircraft Propellers, 
Aerospace Engineering Department, US Naval Academy, Annapolis, 
Maryland, Report EW-10-88, August 1988. 

11. Tanner, James, Flight Test of Half-Scale Pioneer, Master's Thesis, Naval 
Postgraduate School, Monterey, Califomia, March 1989. 



64 



12. Roberts, Sean C, Light Aircraft Performance, Notes, AE 4323, Naval 
Postgratiiate School. Monterey, California, Spring 1988. 

13. Anderson, John, Introduction to Flight, McGraw-Hill, 1985. 

14. Holman, J.P., Experimental Methods for Engineers, McGraw Hill, 1984. 



65 



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c/o Academy of Model Aeronautics 
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66 



9. Mr. Harry Berman 

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Flight test method de- 
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Thesis 
B1085 



Bamichas 

jlight test method de- 
velopment for a quarter- 
scale aircraft with 
minimum instrumentation.